Error in N Queens Problem using Backtracking and Recursion

Question

I first implemented a zero matrix indicating that all the positions of the chessboard are initially available

n=int(input())
answer=[]
restrictedIndices=[[0 for i in range(n)] for j in range(n)]
dp(n,0,restrictedIndices,answer)

and then I implemented three functions to fill the restrictedIndices

def columnFill(restrictedIndices,row,column,n):
    o=column
    restrictedIndices[row][o]=1
    while o+1<n:
        o+=1
        restrictedIndices[row][o]=1
    o=column
    while o-1>=0:
        o-=1
        restrictedIndices[row][o]=1    
    o=column
    return restrictedIndices


def rowFill(restrictedIndices,row,column,n):
    o=row
    restrictedIndices[o][column]=1
    while o+1<n:
        o+=1
        restrictedIndices[o][column]=1
    o=row
    while o-1>=0:
        o-=1
        restrictedIndices[o][column]=1
    o=row    
    return restrictedIndices


def diagonalFill(restrictedIndices,row,column,n):
    o=row
    p=column
    restrictedIndices[o][column]=1
    while o+1<n and p+1<n:
        o+=1
        p+=1
        restrictedIndices[o][p]=1
    o=row
    p=column
    while o-1>=0 and p+1<n:
        o-=1
        p+=1
        restrictedIndices[o][p]=1
    o=row
    p=column
    while o+1<n and p-1>=0:
        o+=1
        p-=1
        restrictedIndices[o][p]=1
    o=row
    p=column
    while o-1>=0 and p-1>=0:
        o-=1
        p-=1
        restrictedIndices[o][p]=1    
    o=row
    p=column
    return restrictedIndices

and then the recursive function

def dp(n,row,restrictedIndices,answer):
    print(restrictedIndices)
    if row==n:
        print("yes i got a solution")
        return -1
    print(restrictedIndices)
    for i in range(n):
        if restrictedIndices[row][i]==1:
            print("rejected",(row,i))
            continue
        
        else:
            x=[i for i in restrictedIndices]
            print(row,i)
            columnFill(restrictedIndices,row,i,n)
            rowFill(restrictedIndices,row,i,n)
            diagonalFill(restrictedIndices,row,i,n)
            dp(n,row+1,restrictedIndices,answer)

I am getting wrong output and I would kindly like to know if we can solve the problem this way and if there is a better alternative. I hope I could understand how recursion and Backtracking works through the solution

score 1 · Accepted Answer · answered May 24 '21 at 16:11

This will not work, because of the following issues:

answer is never populated: it can therefore be nothing else than its initial value, an empty list
Although you let dp return -1 when a solution is found, this value is never checked by the caller. So the caller does not know about it and goes to the next iteration of its for loop
When the recursive call of dp returns, the restrictedIndices list is not returned to its previous state. This means that in the next iterations of the for loop the condition [row][i]==1 will always be True -- this cell was set to 1 during the first iteration. You should make sure that each iteration of the for loop starts with the exact same state of restrictedIndices.

I will not post a working solution, as this is extensively documented on the internet, and recursive solutions for Python can be found also on Stack Overflow:

Error in N Queens Problem using Backtracking and Recursion

1 Answers1